📘 IB Mathematics: Analysis & Approaches HL
IB Mathematics: Analysis and Approaches HL is a demanding and intellectually rewarding course for students with a strong interest in abstract mathematics, logic, and theoretical problem-solving. It’s perfect for those planning to pursue university studies in fields such as mathematics, physics, engineering, or computer science.
This HL course goes beyond the SL curriculum, diving deeper into mathematical theory, proof, and modeling. It challenges students to apply rigorous reasoning and develop powerful analytical thinking skills.
📘 What You’ll Master
- In-depth algebra, polynomial functions, and complex numbers
- Advanced calculus including differential equations and integrals
- Mathematical induction, binomial expansions, and series
- Proof-based reasoning and abstract thinking
- Modeling and real-world problem analysis
🎯 Course Highlights
- Designed for highly analytical and motivated students
- Excellent preparation for mathematically rigorous university courses
- Includes additional HL-only content and extended assessment tasks
📗 Workbook Support
Practice with the Alphy Mathematics: Analysis and Approaches HL Student Workbook to sharpen your skills through advanced problems, IB exam-style questions, and guided support for your Internal Assessment (IA).
Course Features
- Lectures 81
- Quiz 0
- Duration 40 weeks
- Skill level All levels
- Language English
- Students 5489
- Certificate No
- Assessments Yes
- 5 Sections
- 81 Lessons
- 40 Weeks
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- Unit 1. Number and algebra15
- 1.1Scientific notation AA HL
- 1.2Arithmetic sequences and series AA HL
- 1.3Geometric sequences and series AA HL
- 1.4Financial applications AA HL
- 1.5Exponents and logarithms AA HL
- 1.6Deduction AA HL
- 1.7Infinite geometric sequences AA HL
- 1.8The binomial theorem AA HL
- 1.9Counting principles AA HL
- 1.10Partial fractions AA HL
- 1.11Complex numbers AA HL
- 1.12Complex numbers different forms AA HL
- 1.13Powers and roots of complex numbers AA HL
- 1.14Proof by induction and Contradiction AA HL
- 1.15Systems of linear equations AA HL
- Unit 2. Functions15
- 2.1Straight lines AA HL
- 2.2Functions AA HL
- 2.3Graphs and Key features of functions AA HL
- 2.4Composite and inverse functions AA HL
- 2.5The quadratic function AA HL
- 2.6Quadratic equations and quadratic inequalities AA HL
- 2.7Rational functions AA HL
- 2.8Exponential functions AA HL
- 2.9Solving equations AA HL
- 2.10Transformations of graphs AA HL
- 2.11Polynomial functions AA HL
- 2.12Further rational functions AA HL
- 2.13Odd and even functions AA HL
- 2.14Solving inequalities AA HL
- 2.15Further graph transformations AA HL
- Unit 3. Geometry and trigonometry18
- 3.1Three-dimensional space AA HL
- 3.2Triangle trigonometry AA HL
- 3.3Applications of trigonometry AA HL
- 3.4The circle AA HL
- 3.5Trigonometric ratios beyond acute angles AA HL
- 3.6Trigonometric identities AA HL
- 3.7Circular functions AA HL
- 3.8Trigonometric equations AA HL
- 3.9Inverse trigonometric functions AA HL
- 3.10Trigonometric identities AA HL
- 3.11Further circular functions AA HL
- 3.12Vectors AA HL
- 3.13Scalars AA HL
- 3.14Lines in two and three dimensions AA HL
- 3.15Relative positions of lines AA HL
- 3.16Vector product AA HL
- 3.17Vector equations of a plane AA HL
- 3.18Angles between lines and planes AA HL
- Unit 4. Probability and statistics14
- 4.1Collection of data and sampling AA HL
- 4.2Presentation of data AA HL
- 4.3Measures of central tendency AA HL
- 4.4Linear correlation of bivariate data AA HL
- 4.5Probability and expected outcomes AA HL
- 4.6Probability calculations AA HL
- 4.7Discrete random variables AA HL
- 4.8The binomial distribution AA HL
- 4.9The normal distribution and curve AA HL
- 4.10Further linear regression AA HL
- 4.11Conditional probability AA HL
- 4.12The standard normal distribution AA HL
- 4.13Bayes’ theorem AA HL
- 4.14Continuous random variables AA HL
- Unit 5. Calculus19
- 5.1Introduction to differentiation AA HL
- 5.2Increasing and decreasing functions AA HL
- 5.3Derivatives of power functions AA HL
- 5.4Tangents and normals AA HL
- 5.5Introduction to integration AA HL
- 5.6Differentiation rules AA HL
- 5.7Further graph properties AA HL
- 5.8Optimisation AA HL
- 5.9Kinematics AA HL
- 5.10Indefinite integrals AA HL
- 5.11Definite integrals AA HL
- 5.12Limits and continuity AA HL
- 5.13Limits of indeterminate forms AA HL
- 5.14Applications of differentiation AA HL
- 5.15Further differentiation AA HL
- 5.16Further integration AA HL
- 5.17Area and volume AA HL
- 5.18Differential equations AA HL
- 5.19Maclaurin and Taylor series expansions AA HL
